Mathematical modelling of the efficacy and toxicity of cancer chemotherapy

Abstract

From available literature, there is strong evidence that the growth of tumours is to a great extent influenced by the cellular response of the immune system in addition to the therapy administered. While chemotherapy treatment is very effective in killing cancer cells, the levels of toxicity associated with it affects other body cells negatively, the worst of which are cells with higher rate of multiplication and regeneration. A lot of research, with impressive results has been carried out in cancer for the past over four decades, yet there is still not a universally accepted effective mathematical model that provides a way of optimizing chemotherapy efficacy and toxicity.The mathematical model developed in this research has provided a theoretical understanding of the interactions among cancer cells and body cells for cancer patients as well as laying the stage for future research work. Based on the findings from reviewed biological literature, a mathematical model comprising of six ODEs describing the growth of tumour cells while incorporating the immune system response and chemotherapy treatment was formulated and analyzed both analytically and numerically. Three scenarios are presented namely: no tumour with no treatment, tumour with no treatment and tumour with treatment. In the first case (no tumour and no treatment), the system was found to be stable. The tumour with no treatment equilibrium was on the other hand was found be unstable implying that the immune system cannot eliminate cancer cells on their own.Lastly, the case of tumour with treatment was found to be stable hence longer survival times for the patients receiving chemotherapy treatment. When however, the concentration of chemotherapy was increased, the system goes back to instability due to the decline of the number of NK and CD8+ T-cells as a result of chemotherapeutic toxicity.According to the results of the formulated mathematical model, treatment regimens consisting of right concentrations of chemotherapy is effective in eliminating the tumour cell population. Further research should therefore focus on developing models that quantify the optimal drug concentration for maximum efficacy on tumour cells with minimal toxicity to immune cells.